I think what this thread has really shown is that many people who have real objections to HE haven't actually a. met many HErs or b. tried it yourself.
There's a lot of theorising without knowledge. Until you try it, you don't know. Like so many other parenting things, how people think things work and how they do work differs.
I understand why people are concerned about abuse because I can see that if you don't understand how the HE community works, you would be worried.
I don't think that HErs are helping ourselves either by getting all defensive and "how dare you suggest we are all abusers" (not directed at anyone here btw).
If you look at HE law then yes, it looks like a ripe place for abuse. Abuse among HErs who are part of the community is, I think quite rare though. And the reason for that is simple. Its a close knit community, far more than in school. A struggling family who asked for support on their local facebook group would almost certainly get it. Its a very child centered atmosphere and pretty well absolutely anti-smacking, anti-emotional belittling, etc (in the UK-not bible belters). And also, families spend a lot of time with other families-days at a time. I am not saying that means abuse doesn't happen, it happens everywhere, but I would say HE culture is very conducive to preventing abuse.
I also think there are much easier, simpler ways to keep tabs on HE kids. One reason HE'd kids are under the radar is because there is no funding at all for them, so they just don't interact with government-run services. We've had to have routine medical tests and jabs done privately, for instance, because my GP could not get them done via referral. Fund HE groups and give them a space to meet.
But also, putting a kid though school is something like £3600 a year (varies hugely). Offer registered HErs a small percentage of that, say £500, and require it to be spent on educational equipment or similar, and to have a detailed chat with someone say once a year, and the government would quickly have a list of registered HErs and high levels of cooperation. Yes some HErs would refuse to participate on principle-but as a rule, these are high profile, well known people in the community and they are low risk.
The situation at the moment is that HErs don't have to be inspected but if they are, if the reports are correct, the inspectors used very often do not understand HE. If inspectors were genuinely helpful and supportive and actually had the power to offer something, like a free room for a teacher-parent to offer a biology GCSE class, there would be much higher levels of co-operation from HErs. IMO.